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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Overview of the Miniature Sensor Technology Integration (MSTI) spacecraft attitude control system

Msti2 is a small, 164 kg (362 lb), 3-axis stabilized, low-Earth-orbiting satellite whose mission is missile booster tracking. The spacecraft is actuated by 3 reaction wheels and 12 hot gas thrusters. It carries enough fuel for a projected life of 6 months. The sensor complement consists of a Horizon Sensor, a Sun Sensor, low-rate gyros, and a high rate gyro for despin. The total pointing control error allocation is 6 mRad (.34 Deg), and this is while tracking a target on the Earth's surface. This paper describes the Attitude Control System (ACS) algorithms which include the following: attitude acquisition (despin, Sun and Earth acquisition), attitude determination, attitude control, and linear stability analysis.

Mcewen, Rob↗
NASA NTRS1996

Initial Usability Testing of a Hand-Held Electronic Logbook Prototype for the Human Research Facility

The Apple(R) Newton(TM) MessagePad 110 was flown aboard the KC-135 reduced gravity aircraft for microgravity usability testing. The Newton served as the initial hand-held electronic logbook prototype for the International Space Station (ISS) Human Research Facility (HRF). Subjects performed three different tasks with the Newton: (1) using the stylus to tap on different sections of the screen in order to launch an application and to select options within it; (2) using the stylus to write, and; (3) correcting handwriting recognition errors in a handwriting-intensive application. Subjects rated handwriting in microgravity 'Borderline' and had great difficulties finding a way in which to adequately restrain themselves at the lower body in order to have their hands free for the Newton. Handwriting recognition was rated 'Unacceptable,' but this issue is hardware-related and not unique to the microgravity environment. It is suggested that the restraint and handwriting issues are related and require further joint research with the current Handheld Electronic Logbook prototype: the Norand Pen*key Model #6300.

Berman, Andrea H.↗
NASA NTRS1997

Dynamics Questions Associated with the AERCam Sprint Free-Flyer

The International Space Station will require the development of small robotic vehicles for such tasks as external inspection, monitoring of extravehicular activities (EVA's) and station build-up, and providing additional lighting at EVA worksites. The Autonomous EVA Robotic Camera (AERCam) family of free-flyers is currently being developed at NASA Johnson Space Center to perform these functions; the first member of the family is the AERCam Sprint vehicle. Many interesting dynamical questions are associated with the Sprint free-flyer. For instance, the reaction of a vehicle which is nearly spherically symmetric (such as Sprint) to a stuck-on thruster is significantly more complicated than that obtained for an idealized, perfectly spherical, spacecraft model. In particular, the real spacecraft will experience a form of forced nutation, with convergence towards either its major or minor principal axis, depending on both the applied torque and the mass properties of the vehicle. Furthermore, the body-fixed jet force vector may have a significant component along this principal axis, so giving rise to a considerable net linear acceleration of the spacecraft. The large velocity that can result is very important, as it may lead to collision with the nearby Orbiter, and is completely overlooked in the idealized analysis. This report will firstly briefly describe the stuck-on thruster dynamics of the real vehicle, and outline how the small products of inertia of the spacecraft determine the time constants of the motion. Secondly, the dynamical effects of a failed-off jet on the Sprint free-flyer will be described in more detail, and compared with the stuck-on thruster case. This will help to show whether the two malfunctions should be dealt with differently in flight. Finally, the stuck-on thruster detection software (known as the uncommanded motion algorithm) that is proposed to be flown on the Sprint vehicle will be analyzed, and all possible perturbation sources that may tend to give rise to false stuck-on thruster alarms quantified. It will be shown that false alarms can be triggered by discrete events such as a failed-off thruster, a glancing collision with Orbiter structure, or thruster saturation. They can also be triggered by a combination of errors introduced by constantly present sources such as thrust level errors, thruster misalignment, inertial cross-coupling, angular rate sensor noise, and structural vibrations induced by thruster firings. Based on this fact, the original plan to have the spacecraft enter safe mode whenever the uncommanded motion algorithm is triggered does not appear to be advisable. A better approach seems to be to provide the Sprint pilot with a warning whenever uncommanded motion is detected, and then allow the crew to determine whether safing the vehicle is appropriate.

Williams, Trevor↗
NASA NTRS1996

Evaluation of IGS Orbits with Satellite Laser Ranging

The accuracy with which orbits for the Global Positioning System (GPS) spacecraft, can be computed directly affects the accuracy of the resulting site coordinates and polar motion. Several groups routinely analyze GPS ground tracking data to compute precise orbits and terrestrial reference frame solutions. In this paper, we infer the accuracy of the orbits of two of the GPS satellites by comparing to independent laser ranges of subcentimeter accuracy obtained by a small but reasonably well distributed network of tracking sites. We find that all seven International GPS Service for Geodynamics (IGS) analysis centers achieve range residual root mean square (rms) errors at or below the 100 mm level. The best orbit solutions, from JPL, CODE, and the IGS combined product, yield a residual rms of about 50 mm. These residuals are consistent with three dimensional orbit errors of less than 150 mm. Estimating yaw rates for the spacecraft during shadow events, and using these estimates to compute the laser residual, significantly improves the fit. A small mean residual value of -15 to -30 mm seems to exist for most centers and laser sites which is not fully explained at present, but may be due to uncertainties in the corrections to the laser data, such as the reflector to spacecraft center of mass vector or small reference frame differences between the SLR sites and the GPS orbits.

Watkins, M. M.↗
NASA NTRS2000

Measuring Postglacial Rebound with GPS and Absolute Gravity

We compare vertical rates of deformation derived from continuous Global Positioning System (GPS) observations and episodic measurements of absolute gravity. We concentrate on four sites in a region of North America experiencing postglacial rebound. The rates of uplift from gravity and GPS agree within one standard deviation for all sites. The GPS vertical deformation rates are significantly more precise than the gravity rates, primarily because of the denser temporal spacing provided by continuous GPS tracking. We conclude that continuous GPS observations are more cost efficient and provide more precise estimates of vertical deformation rates than campaign style gravity observations where systematic errors are difficult to quantify.

Larson, Kristine M.↗
NASA NTRS2000

Improved Correction System for Vibration Sensitive Inertial Angle of Attack Measurement Devices

Inertial angle of attack (AoA) devices currently in use at NASA Langley Research Center (LaRC) are subject to inaccuracies due to centrifugal accelerations caused by model dynamics, also known as sting whip. Recent literature suggests that these errors can be as high as 0.25 deg. With the current AoA accuracy target at LaRC being 0.01 deg., there is a dire need for improvement. With other errors in the inertial system (temperature, rectification, resolution, etc.) having been reduced to acceptable levels, a system is currently being developed at LaRC to measure and correct for the sting-whip-induced errors. By using miniaturized piezoelectric accelerometers and magnetohydrodynamic rate sensors, not only can the total centrifugal acceleration be measured, but yaw and pitch dynamics in the tunnel can also be characterized. These corrections can be used to determine a tunnel's past performance and can also indicate where efforts need to be concentrated to reduce these dynamics. Included in this paper are data on individual sensors, laboratory testing techniques, package evaluation, and wind tunnel test results on a High Speed Research (HSR) model in the Langley 16-Foot Transonic Wind Tunnel.

Crawford, Bradley L.↗
NASA NTRS2008

Gamma-Ray Emision from the Broad-Line Radio Galaxy 3C 111

The broad-line radio galaxy 3C 111 has been suggested as the counterpart of the Gamma-ray source 3EGJ0416+3650. While 3C 111 meets most of the criteria for a high-probability identification, like a bright fla t-spectrum radio core and a blazarlike broadband SED, in the Third EG RET Catalog, the large positional offset of about 1.5 degrees put 3C1 11 outside the 99% probability region for 3EG J0416+3650, making this association questionable. We present a re-analysis of all available data for 3C111 from the EGRET archives, resulting in probable detection of high-energy Gamma-ray emission above 1000MeV from a position clo se to the nominal position of 3C 111, in two separate viewing periods (VPs), at a 3sigma level in each. A new source, GROJ0426+3747, appea rs to be present nearby, seen only in the >1000MeV data. For >100MeV, the data are in agreement with only one source (at the original cata log position) accounting for most of the EGRET-detected emission of 3 EGJ0416+3650. A follow-up Swift UVOT/XRT observation reveals one mode rately bright X-ray source in the error box of 3EGJ0416+3650, but bec ause of the large EGRET position uncertainty, it is not certain that the X-ray and Gamma-ray sources are associated. A Swift observation of GROJ0426+3747 detected no X.ray source nearby.

Hartman, Robert C.↗
NASA NTRS2007

Portable Microleak-Detection System

The figure schematically depicts a portable microleak-detection system that has been built especially for use in testing hydrogen tanks made of polymer-matrix composite materials. (As used here, microleak signifies a leak that is too small to be detectable by the simple soap-bubble technique.) The system can also be used to test for microleaks in tanks that are made of other materials and that contain gases other than hydrogen. Results of calibration tests have shown that measurement errors are less than 10 percent for leak rates ranging from 0.3 to 200 cm3/min. Like some other microleak-detection systems, this system includes a vacuum pump and associated plumbing for sampling the leaking gas, and a mass spectrometer for analyzing the molecular constituents of the gas. The system includes a flexible vacuum chamber that can be attached to the outer surface of a tank or other object of interest that is to be tested for leakage (hereafter denoted, simply, the test object). The gas used in a test can be the gas or vapor (e.g., hydrogen in the original application) to be contained by the test object. Alternatively, following common practice in leak testing, helium can be used as a test gas. In either case, the mass spectrometer can be used to verify that the gas measured by the system is the test gas rather than a different gas and, hence, that the leak is indeed from the test object.

Rivers, H. Kevin↗
NASA NTRS2012

Real-Time X-ray Radiography Diagnostics of Components in Solid Rocket Motors

Solid rocket motors (SRMs) typically use nozzle materials which are required to maintain their shape as well as insulate the underlying support structure during the motor operation. In addition, SRMs need internal insulation materials to protect the motor case from the harsh environment resulting from the combustion of solid propellant. In the nozzle, typical materials consist of high density graphite, carbon-carbon composites and carbon phenolic composites. Internal insulation of the motor cases is typically a composite material with carbon, asbestos, Kevlar, or silica fibers in an ablative matrix such as EPDM or NBR. For both nozzle and internal insulation materials, the charring process occurs when the hot combustion products heat the material intensely. The pyrolysis of the matrix material takes away a portion of the thermal energy near the wall surface and leaves behind a char layer. The fiber reinforcement retains the porous char layer which provides continued thermal protection from the hot combustion products. It is of great interest to characterize both the total erosion rates of the material and the char layer thickness. By better understanding of the erosion process for a particular ablative material in a specific flow environment, the required insulation material thickness can be properly selected. The recession rates of internal insulation and nozzle materials of SRMs are typically determined by testing in some sort of simulated environment; either arc-jet testing, flame torch testing, or subscale SRMs of different size. Material recession rates are deduced by comparison of pre- and post-test measurements and then averaging over the duration of the test. However, these averaging techniques cannot be used to determine the instantaneous recession rates of the material. Knowledge of the variation in recession rates in response to the instantaneous flow conditions during the motor operation is of great importance. For example, in many SRM configurations the recession of the solid propellant grain can drastically alter the flow-field and effect the recession of internal insulation and nozzle materials. Simultaneous measurement of the overall erosion rate, the development of the char layer, and the recession of the char-virgin interface during the motor operation can be rather difficult. While invasive techniques have been used with limited success, they have serious drawbacks. Break wires or make wire sensors can be installed into a sufficient number of locations in the charring material from which a time history of the charring surface can be deduced. These sensors fundamentally alter the local structure of the material in which they are imbedded. Also, the location of these sensors within the material is not known precisely without the use of an X-ray. To determine instantaneous recession rates, real-time X-ray radiography (X-ray RTR) has been utilized in several SRM experiments at PSU. The X-ray RTR system discussed in this paper consists of an X-ray source, X-ray image intensifier, and CCD camera connected to a capture computer. The system has been used to examine the ablation process of internal insulation as well as nozzle material erosion in a subscale SRM. The X-ray source is rated to 320 kV at 10 mA and has both a large (5.5 mm) and small (3.0 mm) focal spot. The lead-lined cesium iodide X-ray image intensifier produces an image which is captured by a CCD camera with a 1,000 x 1,000 pixel resolution. To produce accurate imagery of the object of interest, the alignment of the X-ray source to the X-ray image intensifier is crucial. The image sequences captured during the operation of an SRM are then processed to enhance the quality of the images. This procedure allows for computer software to extract data on the total erosion rate and the char layer thickness. Figure 1 Error! Reference source not found.shows a sequence of images captured during the operation the subscale SRM with the X-ray RTR system. The X-rayTR system, alignment procedure, uncertainty determination, and image analysis process will be discussed in detail in the full manuscript.

Cortopassi, A. C.↗
NASA NTRS2013

The Microwave Temperature Profiler (PERF)

The JPL developed Microwave Temperature Profiler (MTP) has recently participated in GloPac, HIPPO (I to V) and TORERO, and the ongoing ATTREX campaigns. The MTP is now capable of supporting the NASA Global Hawk and a new canister version supports the NCAR G-V. The primary product from the MTP is remote measurements of the atmospheric temperature at, above and below the flight path, providing for the vertical state of the atmosphere. The NCAR-MTP has demonstrated unprecedented instrument performance and calibration with plus or minus 0.2 degrees Kelvin flight level temperature error. Derived products include curtain plots, isentropes, lapse rate, cold point height and tropopause height.

airborne instruments↗
NASA NTRS2016

Evaluating Model Parameterizations of Submicron Aerosol Scattering and Absorption with in situ Data from ARCTAS 2008

Accurate modeling of the scattering and absorption of ultraviolet and visible radiation by aerosols is essential for accurate simulations of atmospheric chemistry and climate. Closure studies using in situ measurements of aerosol scattering and absorption can be used to evaluate and improve models of aerosol optical properties without interference from model errors in aerosol emissions, transport, chemistry, or deposition rates. Here we evaluate the ability of four externally mixed, fixed size distribution parameterizations used in global models to simulate submicron aerosol scattering and absorption at three wavelengths using in situ data gathered during the 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) campaign. The four models are the NASA Global Modeling Initiative (GMI) Combo model, GEOS-Chem v9- 02, the baseline configuration of a version of GEOS-Chem with online radiative transfer calculations (called GC-RT), and the Optical Properties of Aerosol and Clouds (OPAC v3.1) package. We also use the ARCTAS data to perform the first evaluation of the ability of the Aerosol Simulation Program (ASP v2.1) to simulate submicron aerosol scattering and absorption when in situ data on the aerosol size distribution are used, and examine the impact of different mixing rules for black carbon (BC) on the results. We find that the GMI model tends to overestimate submicron scattering and absorption at shorter wavelengths by 10-23 percent, and that GMI has smaller absolute mean biases for submicron absorption than OPAC v3.1, GEOS-Chem v9-02, or GC-RT. However, the changes to the density and refractive index of BC in GCRT improve the simulation of submicron aerosol absorption at all wavelengths relative to GEOS-Chem v9-02. Adding a variable size distribution, as in ASP v2.1, improves model performance for scattering but not for absorption, likely due to the assumption in ASP v2.1 that BC is present at a constant mass fraction throughout the aerosol size distribution. Using a core-shell mixing rule in ASP overestimates aerosol absorption, especially for the fresh biomass burning aerosol measured in ARCTAS-B, suggesting the need for modeling the time-varying mixing states of aerosols in future versions of ASP.

Alvarado, Matthew J.↗
DOE OSTI2019

A Simple Hybrid Electric Vehicle Fuel Consumption Model for Transportation Applications(DOI: 10.5772/intechopen.89055)

This study presents a simple power-based microscopic hybrid electric vehicle (HEV) fuel consumption model for use in microscopic traffic software and various connected and automated vehicle (CAV) applications, including eco-routing and eco-drive systems. While numerous HEV energy consumption models have been developed, these models are complex and require vehicle engine data deeming them difficult to implement and making them nontransferable. The proposed model was developed using empirical data for a 2010 Toyota Prius—the most popular HEV. The model was then extended to other HEVs thus extending the domain of application of the model. The proposed fuel consumption model estimates the instantaneous fuel consumption rates of an HEV using instantaneous vehicle operational input variables, including the vehicle’s speed, acceleration, and roadway grade, which can be acquired from global positioning system (GPS) equipment or other sensors. The model estimates vehicle fuel consumption rates consistent with empirical data producing an average error of 2.1% for the Toyota Prius and up to 4% for other HEVs demonstrating the applicability and transferability of the model to various HEVs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Fault Characterization and Diagnostics Supporting Condition-Based Operation and Maintenance of Gas Turbine Engines

Condition-Based Operation and Maintenance (CBOM) is the state-of-the-art in maintenance approaches for gas turbine engines. CBOM applies engine sensor information to the optimization of future operation and maintenance procedures; this technique reduces costs for engine operators by minimizing unplanned outages and catastrophic engine degradation. However, due to the complexities of gas turbine operation and the lack of available engine sensors, further development is required to fully realize the benefits of CBOM. In the turbine section, rotating components interact with high temperature flows, which creates intense thermal and mechanical stresses. As a result, there are numerous mechanisms of component degradation in the turbine section. Furthermore, turbine components – like stator vanes and rotor blades – are among the most expensive in the engine because they are complex to design and manufacture. For these reasons, this dissertation addresses two main questions: (i) which parameters or faults within the turbine section are most important to monitor, and (ii) how can these parameters or faults be monitored in an engine-relevant environment? Although many turbine parameters and faults have been investigated in the open literature, there are some faults that are still not well understood. Rotor-casing eccentricity, which causes a non-constant blade tip clearance around the annulus, has not been investigated in terms of its effects on turbine efficiency. Therefore, the first study in this dissertation quantifies overall and local turbine efficiency for varying levels of rotor-casing eccentricity. Results showed negligible variations to overall turbine efficiency, meaning rotor-casing eccentricity only becomes relevant to CBOM when its severity causes rotordynamic issues. Purge flow is critical to turbine hardware longevity because it prevents ingestion of hot main gas path (MGP) flow into the under-platform regions. Despite its importance, there are currently no methods for monitoring purge flow performance in an engine environment. Therefore, the second study in this dissertation develops a predictive model for sealing effectiveness using inputs from two fast-response pressure sensors. Results exhibited low prediction errors across a full range of purge flow rates, which supports the viability of the modelling approach for CBOM. The final two studies in this dissertation address blade coolant flow monitoring. This cooling flow is responsible for protecting the turbine blades from the MGP flow, which exits the combustor at temperatures greater than the blade melting point. These studies showed that temperature measurements on the blade surface can be used to accurately predict blade coolant flow rate, and that defining the candidate features relative to the coolant trajectory is important for maintaining accuracy as coolant flow rate degradation occurs. This work enables blade coolant flow monitoring, which is currently not possible through existing condition monitoring techniques.

condition-based, gas turbines, diagnostics,↗
DOE OSTI2013

DOMINO: A fast 3D cartesian discrete ordinates solver for reference PWR simulations and SPN validation

As part of its activity, EDF R and D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SPN) method to compute the neutron flux inside the core for eigenvalue calculations. In order to assess the accuracy of SPN calculations, we have developed DOMINO, a new 3D Cartesian SN solver. The parallel implementation of DOMINO is very efficient and allows to complete an eigenvalue calculation involving around 300 x 10{sup 9} degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S{sub 8} 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP{sub 5} DIABOLO fission production rate is lower than 0.2% compared to the S{sub 8} DOMINO reference for this 3D PWR core model. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS2004

Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the 1-D Kinetic Model

Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the 1-D Poisson equation for EC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with non-fusing hydrogen-1. The deuterium rates are consistent with predictions from the model.

Dobson, Chris C.↗
DOE OSTI2026

Updating PV and Battery Bill Savings Calculations for Net Billing: New Best Practices for Input Data and Uncertainty

Jurisdictions are increasingly adopting compensation structures for distributed PV and PV-battery systems that price exported energy lower than energy consumed onsite (net billing rates). Standard methods for calculating the bill savings from PV and PV-battery systems were developed for net metering structures, and applying these same methods to net billing structures (such as using Typical Meteorological Year weather with actual year load) introduces bias errors that underestimate PV-battery system bill savings by between 1.5\% and 9\%, depending on the utility rate. We assess the magnitude of these errors and compare them to other sources of uncertainty when estimating the bill savings from PV and PV-battery systems under more complex utility rates.

14 SOLAR ENERGY↗
DOE OSTI2014

SU-D-18C-04: The Feasibility of Quantifying MRI Contrast Agent in Pulsatile Flowing Blood Using DCE-MRI

Purpose: To assess the feasibility of accurately quantifying the concentration of MRI contrast agent (CA) in pulsatile flowing blood by measuring its T{sub 1}, as is common for the purposes of obtaining a patientspecific arterial input function (AIF). Dynamic contrast enhanced (DCE) - MRI and pharmacokinetic (PK) modelling is widely used to produce measures of vascular function but accurate measurement of the AIF undermines their accuracy. A proposed solution is to measure the T{sub 1} of blood in a large vessel using the Fram double flip angle method during the passage of a bolus of CA. This work expands on previous work by assessing pulsatile flow and the changes in T{sub 1} seen with a CA bolus. Methods: A phantom was developed which used a physiological pump to pass fluid of a known T{sub 1} (812ms) through the centre of a head coil of a clinical 1.5T MRI scanner. Measurements were made using high temporal resolution sequences suitable for DCE-MRI and were used to validate a virtual phantom that simulated the expected errors due to pulsatile flow and bolus of CA concentration changes typically found in patients. Results: : Measured and virtual results showed similar trends, although there were differences that may be attributed to the virtual phantom not accurately simulating the spin history of the fluid before entering the imaging volume. The relationship between T{sub 1} measurement and flow speed was non-linear. T{sub 1} measurement is compromised by new spins flowing into the imaging volume, not being subject to enough excitations to have reached steady-state. The virtual phantom demonstrated a range of recorded T{sub 1} for various simulated T{sub 1} / flow rates. Conclusion: T{sub 1} measurement of flowing blood using standard DCE-MRI sequences is very challenging. Measurement error is non-linear with relation to instantaneous flow speed. Optimising sequence parameters and lowering baseline T{sub 1} of blood should be considered.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1990

Frame synchronization for a channel with different data rates

In some communication links, different data rates are used at different times on the same channel and each is assigned a separate frame synchronization (sync) marker. The frame search is completed within a finite number of frame intervals once both phase-lock and bit-sync are achieved because the incoming data rate can change. The probability of failure to frame-lock, and an upper bound of probability of false frame-lock in a frame search mode are derived for a communication link with a 10 to the -5th bit error probability. The probability of failure to detect data-rate change and the probability of false detection of data-rate change in a frame-lock mode are discussed. In a frame-lock mode, the probability of failure to detect data-rate change and probability detection of data-rate change an equal to 4.96 x 10 to the -12th. A frame-lock device can be used for the Space Station Freedom Ku-band return link.

Kwon, Hyuck M.↗

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